Label |
Class |
Class size |
Class degree |
Base field |
Field degree |
Field signature |
Conductor |
Conductor norm |
Discriminant norm |
Root analytic conductor |
Bad primes |
Rank |
Torsion |
CM |
CM |
Sato-Tate |
$\Q$-curve |
Base change |
Semistable |
Potentially good |
Nonmax $\ell$ |
mod-$\ell$ images |
$Ш_{\textrm{an}}$ |
Tamagawa |
Regulator |
Period |
Leading coeff |
j-invariant |
Weierstrass coefficients |
Weierstrass equation |
3872.14-b1 |
3872.14-b |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
3872.14 |
\( 2^{5} \cdot 11^{2} \) |
\( 2^{18} \cdot 11^{6} \) |
$1.86497$ |
$(a), (-a+1), (-2a+3), (2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$1.461921226$ |
2.210217144 |
\( -\frac{46830231}{234256} a + \frac{212077575}{117128} \) |
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 12 a - 20\) , \( 11 a - 9\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(12a-20\right){x}+11a-9$ |
3872.5-b1 |
3872.5-b |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
3872.5 |
\( 2^{5} \cdot 11^{2} \) |
\( 2^{18} \cdot 11^{6} \) |
$1.86497$ |
$(a), (-a+1), (-2a+3), (2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{7} \) |
$1$ |
$1.461921226$ |
2.210217144 |
\( -\frac{46830231}{234256} a + \frac{212077575}{117128} \) |
\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -9 a + 23\) , \( 0\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-9a+23\right){x}$ |
5324.6-e1 |
5324.6-e |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
5324.6 |
\( 2^{2} \cdot 11^{3} \) |
\( 2^{6} \cdot 11^{12} \) |
$2.01952$ |
$(a), (-a+1), (-2a+3), (2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1$ |
$0.881571669$ |
2.665622171 |
\( -\frac{46830231}{234256} a + \frac{212077575}{117128} \) |
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( -40 a + 50\) , \( 45 a - 83\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-40a+50\right){x}+45a-83$ |
5324.7-d1 |
5324.7-d |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
5324.7 |
\( 2^{2} \cdot 11^{3} \) |
\( 2^{6} \cdot 11^{12} \) |
$2.01952$ |
$(a), (-a+1), (-2a+3), (2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1$ |
$0.881571669$ |
2.665622171 |
\( -\frac{46830231}{234256} a + \frac{212077575}{117128} \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( 21 a - 64\) , \( -59 a + 50\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(21a-64\right){x}-59a+50$ |
15488.20-d2 |
15488.20-d |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
15488.20 |
\( 2^{7} \cdot 11^{2} \) |
\( 2^{24} \cdot 11^{6} \) |
$2.63746$ |
$(a), (-a+1), (-2a+3), (2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$1.033734412$ |
1.562859530 |
\( -\frac{46830231}{234256} a + \frac{212077575}{117128} \) |
\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( -5 a + 46\) , \( 27 a + 42\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(-5a+46\right){x}+27a+42$ |
15488.5-d2 |
15488.5-d |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
15488.5 |
\( 2^{7} \cdot 11^{2} \) |
\( 2^{24} \cdot 11^{6} \) |
$2.63746$ |
$(a), (-a+1), (-2a+3), (2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$1.033734412$ |
1.562859530 |
\( -\frac{46830231}{234256} a + \frac{212077575}{117128} \) |
\( \bigl[a\) , \( -a - 1\) , \( a\) , \( 33 a - 24\) , \( -7 a + 65\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(33a-24\right){x}-7a+65$ |
23716.5-a2 |
23716.5-a |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
23716.5 |
\( 2^{2} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{6} \cdot 7^{6} \cdot 11^{6} \) |
$2.93392$ |
$(a), (-a+1), (-2a+1), (-2a+3), (2a+1)$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{7} \) |
$0.131842497$ |
$1.105108572$ |
3.524449760 |
\( -\frac{46830231}{234256} a + \frac{212077575}{117128} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -21 a - 16\) , \( -7 a - 22\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(-21a-16\right){x}-7a-22$ |
*The rank, regulator and analytic order of Ш are
not known for all curves in the database; curves for which these are
unknown will not appear in searches specifying one of these
quantities.